73 research outputs found
On the analytical invariance of the semigroups of a quasi-ordinary hypersurface singularity
We associate to any irreducible germ S of complex quasi-ordinary hypersurface
an analytically invariant semigroup. We deduce a direct proof (without passing
through their embedded topological invariance) of the analytical invariance of
the normalized characteristic exponents. These exponents generalize the generic
Newton-Puiseux exponents of plane curves. Incidentally, we give a toric
description of the normalization morphism of the germ S.Comment: 29 page
From singularities to graphs
In this paper I analyze the problems which led to the introduction of graphs
as tools for studying surface singularities. I explain how such graphs were
initially only described using words, but that several questions made it
necessary to draw them, leading to the elaboration of a special calculus with
graphs. This is a non-technical paper intended to be readable both by
mathematicians and philosophers or historians of mathematics.Comment: 23 pages, 27 figures. Expanded version of the talk given at the
conference "Quand la forme devient substance : puissance des gestes,
intuition diagrammatique et ph\'enom\'enologie de l'espace", which took place
at Lyc\'ee Henri IV in Paris from 25 to 27 January 201
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